There are 3 essential components to the equation to solve this problem; we (umpires) have control over 2 of them. The third is under the control of gentlemen like @beerguy55 and @Coach Carl, but I concede, it is highly variable.
The first element, and most immediate and direct, is to not call Time. Stop. Deny (the request, the urge, the temptation, etc.). Resist. Hold fast. Stick to it. Respond to the “requests” with:
“No.”
”Nope”
”(You) don’t need it.”
”Nah”
”No need”
”Noppity noppity nooooo.”
In 94% of cases, our granting of Time is a concession, not a compulsion. In the professional game, the protocol – note, not codified rule – is to call Time, not only to change the baseball (cuz they gots plenty), but because the slightest twitch can result in an Out or an Advanced base, “needlessly”. That’s not part of the “professional game”. This isn’t the case of amateurs, especially of single-digit-age tots. They should be able to throw a ball 10-15 feet, they should be able to catch said ball, they should be able to get themselves up to their feet from a on-butt or on-knees position, and if you say, “but they’re still learning!”, then I’ll immediately counter with, “And experience is the best way to learn!”
The second element is we need Tournament Directors / Site Supervisors / League Admin who will reinforce us and this perspective, rather than kowtow to the bleating, “outraged” coaches, and sabotage us. Games are snappier, with more action, and more experiential learning, than being halted every. two. seconds. because. we. need. time. called. to. give. two. thousand. frenzied. signs. to. an. infield. who. doesn’t. know. exactly. what. to. “do”. anyway.
Coach, you and I, and everyone here know it’s going to be R2-&-R3 in one pitch, regardless of if you have “a play” on or not. Heck, it’ll likely be R2, with a run scored cuz that pitch… vooooop! <clink> … just went over my head clean to the backstop.
Didn’t have that play “on”, didja?
But truly, we need TDs and admins to hold the line, and reply, “That’s the way it is.”, not with, “I’ll talk to him (the umpire)”, or, “Yeah, he’s a stickler about that.”, or, “He won’t be doing your games in the future.” Those replies tolerate and coddle those coaches. Which attribute directly to the third element…
Which is, coaches must stop coaching this (the granting of time) as an entitlement, an expectation, and as a counter-tactic (to aggressive base running). It is not benefitting their charges (kids), nor is it benefitting the game.